Reassessing enzyme kinetics: Considering protease-as- substrate interactions in proteolytic networks Meghan C. Ferrall-Fairbanksa, Chris A. Kieslicha, and Manu O. Platta,1 aWallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA 30332 Edited by G. Marius Clore, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD, and approved December 24, 2019 (received for review July 16, 2019) Enzymes are catalysts in biochemical reactions that, by definition, analyze how these proteases interact cooperatively or antagonis- increase rates of reactions without being altered or destroyed. tically, and researchers have only recently started to investigate However, when that enzyme is a protease, a subclass of enzymes these types of interactions (1, 12–14). that hydrolyze other proteins, and that protease is in a multiprotease Of interest to this work are cathepsins K, L, and S (catK, catL, system, protease-as-substrate dynamics must be included, challenging and catS), which share 60% sequence identity and redundancy in assumptions of enzyme inertness, shifting kinetic predictions of that target substrate proteins with different catalytic activities toward system. Protease-on-protease inactivating hydrolysis can alter pre- different matrix substrates (2, 5, 15). These cathepsins are in- dicted protease concentrations used to determine pharmaceutical volved in a number of diseases and have been targets of phar- dosing strategies. Cysteine cathepsins are proteases capable of maceutical companies to design inhibitors. However, of the 16 cathepsin cannibalism, where one cathepsin hydrolyzes another with inhibitors that have progressed to phase II and III clinical trials, substrate present, and misunderstanding of these dynamics may none have made it to the medicine cabinet (16–18). cause miscalculations of multiple proteases working in one proteolytic Previously, we have shown that, when catK and catS were network of interactions occurring in a defined compartment. Once coincubated together, the total amount of substrate degradation rates for individual protease-on-protease binding and catalysis are from the equimolar amounts of cathepsins was less than the sum determined, proteolytic network dynamics can be explored using of the individual cathepsins’ proteolytic activity (12). The catS computational models of cooperative/competitive degradation by preferentially binding and degrading catK over the substrate was multiple proteases in one system, while simultaneously incorporating introduced and could accurately capture the amount of substrate SYSTEMS BIOLOGY substrate cleavage. During parameter optimization, it was revealed degradation (12), even such that mutating the sites susceptible to that additional distraction reactions, where inactivated proteases cannibalistic cleavage reduced the amount of catK cleaved by become competitive inhibitors to remaining, active proteases, oc- catS, effectively creating cannibalism resistant catK mutants curred, introducing another network reaction node. Taken together, (14). In another study, catK and L interactions were important in improved predictions of substrate degradation in a multiple protease network were achieved after including reaction terms of autodiges- tendon extracellular matrix (ECM) degradation in vivo (19), and tion, inactivation, cannibalism, and distraction, altering kinetic consid- the sequence of cathepsin addition to the system, whether se- erations from other enzymatic systems, since enzyme can be lost to creted by the cells in vivo, or with addition of recombinant proteolytic degradation. We compiled and encoded these dynamics into an online platform (https://plattlab.shinyapps.io/catKLS/)forin- Significance dividual users to test hypotheses of specific perturbations to multiple cathepsins, substrates, and inhibitors, and predict shifts in proteolytic Proteases are enzymes that hydrolyze other proteins, including network reactions and system dynamics. other proteases, which challenges assumptions of enzyme in- ertness in chemical reactions, and alters predicted protease− computational modeling | cysteine cathepsins | extracellular matrix | substrate concentrations using established mass action frame- proteolysis works. Cysteine cathepsins are powerful proteases involved in numerous diseases by cleaving substrates, but they also hy- he implicit assumption of protease inertness, where proteases drolyze each other, requiring inclusion of as yet undefined, Tonly hydrolyze substrate(s) and only negligible degradative protease-as-substrate dynamics. Here, we used experimental interactions occur between proteases in solution, dominates the and computational models to improve predictions of the con- protease literature. However, this assumption must be recon- centrations of multiple species and intermediates generated sidered when considering proteases working as a part of a system during substrate degradation in multiprotease systems by in- or a proteolytic network with multiple classes of proteases, sub- cluding protease-on-protease reactions of autodigestion, inacti- strates, and inhibitors (1). Important work has been done on vation, cannibalism, and distraction in proteolytic networks. This protease families that contain members that hydrolyze each other was made available online for others to test perturbations and to activate zymogens, or inactive forms, converting the inactive predict shifts in proteolytic network reactions and system dynamics (https://plattlab.shinyapps.io/catKLS/). protease to the mature, active protease form, but less so on de- structive hydrolysis that removes a protease from the pool able to Author contributions: M.C.F.-F., C.A.K., and M.O.P. designed research, performed re- actively proteolyze substrate. There are also families of pro- search, analyzed data, and wrote the paper. miscuous proteases such as the cysteine cathepsins, a potent family The authors declare no competing interest. of proteases first identified in lysosomes where they serve im- This article is a PNAS Direct Submission. portant roles in protein turnover, but that have since been Published under the PNAS license. implicated in a number of other intracellular and extracellular Data deposition: All data and the software code are available at Mendeley Data (https:// compartments and are up-regulated in a number of tissue- data.mendeley.com/datasets/k2h7y57sd8/1). The interactive, online interface supporting destructive diseases (2–8). Cysteine cathepsins are synthesized as these findings is available at https://plattlab.shinyapps.io/catKLS/. procathepsins, with a propeptide occluding the active site, which 1To whom correspondence may be addressed. Email: [email protected]. must be cleaved to have mature, active enzyme (2, 3). Propeptide This article contains supporting information online at https://www.pnas.org/lookup/suppl/ cleavage has been reported to occur through autocatalysis, as well doi:10.1073/pnas.1912207117/-/DCSupplemental. as through cleavage by another protease (5, 9–11). It is difficult to First published January 24, 2020. www.pnas.org/cgi/doi/10.1073/pnas.1912207117 PNAS | February 11, 2020 | vol. 117 | no. 6 | 3307–3318 Downloaded by guest on September 23, 2021 enzyme addition in vitro, contributed to total substrate degra- alone could not accurately predict product formation by an indi- dation due to cannibalistic interactions between catK and L (20). vidual cathepsin whether it was catK, L, or S over this time frame To expand upon our knowledge of the cathepsin proteolytic of 120 min, and is represented as the straight line (Fig. 1 F–K). network and its impact on substrate degradation and enzyme Underlying assumptions that the proteases are catalysts that kinetic models, here we developed a mechanistic model con- do not get used or modified in the mass action kinetics over- sisting of a system of ordinary differential equations character- predicted the product formation by cathepsins and required izing the catK, L, and S proteolytic network with elastin and some terms that reduced the amount of active protease, since the gelatin substrates. We use a systematic approach to 1) charac- substrate concentration was not limiting. When a protease can terize the kinetics of individual cathepsins on substrates elastin also be the substrate, as well as the enzyme in the system, there is or gelatin in this system; 2) incorporate cathepsin-on-cathepsin a loss of enzyme over time that must be considered. To accom- binding and catalytic interaction rates for each pair of catK, L, modate this, the model was modified to include terms of auto- and S; and 3) integrate all three cathepsin interaction and sub- digestion, defined as one active cathepsin binding to another strate degradation activities. With this cathepsin proteolytic active cathepsin of the same type and hydrolyzing it, resulting in network model, we predicted substrate degradation a priori of all one free, active cathepsin and one degraded cathepsin (Fig. 1C). three cathepsins at once and simulated the effects of changes to This mechanism has been previously shown to occur for ca- this proteolytic network for additional substrates and for the thepsin family members (9–11). Another mechanism by which genetic disease pycnodysostosis, caused by mutations in the catK active cathepsins are lost to the system is inactivation. Cysteine gene, to demonstrate the utility and importance of considering